∫ ((cos x – sin x)/ (cos x + sin x)× (2 + 2sin 2x) dx
= ∫ (((cos x – sinx)/ (cos x + sinx )) (1 + (sinx + cos x)2)) dx
= ∫ (1 + t2/ t) dt, Let cos x + sin x = t
= (– sin x + cos x) dx = dt
= ∫ (t + (1/t)) dt
= (t2/2) + log |t| + c
= ((sin x + cos x)2/ 2) + log |sin x + cos x| + c